Motion of Vehicles on Unbanked Curved Roads

Motion of Vehicles on Unbanked Curved Roads

• Consider a vehicle moving on a curved unbanked road of radius of curvature ρ as shown in Fig. 9.11.1.

• At large velocities, the vehicle can either skid or overturn which is due to centrifugal force which is in normal direction.

• The F.B.D. of the vehicle is shown in Fig. 9.11.1. with forces in normal and y-direction. Forces are not shown in the tangential direction.

b = Wheel base and

h = Height of C.G from the ground.

• The above equation gives maximum safe velocity without skidding. To increase the maximum safe velocity, the coefficient of friction 'μ' has to be increased by making the road surface rough.

• Increasing coefficient of friction has two problems- it increases the wear and tear of the tyres and it is unreliable as μ will decrease if oil or sand falls on the road.

• For maximum safe velocity without overturning,

• The maximum safe velocity can be increased by increasing the wheel base and decreasing the height of centre of gravity from the ground level as is done in race cars.

Solved Examples for Understanding

Example 9.11.1 

A vehicle of mass 1000 kg is rounding an unbanked horizontal curve of radius 300 m. If the left and right wheels are 1 m apart, C. G. of the vehicle is 0.8 m above the road level and coefficient of friction μ=0.2, find the maximum speed of the vehicle so that level and co it should neither skid nor overturn. For what value of u will the vehicle skid and overturn simultaneously?

Solution: 

For unbanked road, the maximum speed without overturning is

For no overturning,

⸫ Safe speed, which is smaller of the two, is 24.26 m/s = 87.34 km/h.

For simultaneous skidding and overturning.